The new dynamical interaction problems connected with the increasing complexity in spacecraft configuration, with the advent of the Space Shuttle, which has provided the opportunity to perform "in situ" experiments with deployable appendages, and with the assembly of large space structures, as the space station Freedom - to be constructed in international cooperation on the 90's - have attracted the efforts of many scientists to the area of control and dynamical modeling of flexible structures with moving parts.

In the early space missions, the dynamical interactions between flexibility and attitude control were considered as secondary phenomenon. Quickly became clear that they play an important role, being affected by factors like solar radiation and pressure, magnetic and gravitational torques, appendages deployment, etc. and resulting in possible failures of the vehicle to perform all or part of its mission. This remains true even when the vehicle has a very simple configuration, as in the case of the Explorer I (1958) and Alouette I (1962) space crafts.

Equally important for the mission success, is the study of the transient dynamics during the deployment of appendages. Most of the investigators deal with the post deployment behavior, because the study of the deployment phase is much more complex due to the fact that the inertial and geometric properties of the system are time varying. As a result, many simplifications have been introduced to develop methods to deal with the problem.

In this context, this work intends to study the dynamical behavior of a very particular class of space crafts: those which are composed by a central rigid body containing reaction wheels, also assumed to be rigid, and extendible solar arrays, which will be considered flexible only after the deployment phase.

Some basic theoretical aspects, necessary to the dynamical modeling of attitude motion through Lagrangian formulation, are presented for this particular class of vehicles. To avoid the distributed parameters and the hybrid character of the set of motion equations, after obtaining the kinetic, gravitational and elastic potential energies for the Lagrangian function, some simplifications are performed through the use of the Assumed Modes Method for the elastic displacements of the appendages.

During the deployment phase, the variation of the inertia dyadic is analyzed to verify how does the motion of a deployable appendage affects the attitude motion of the spacecraft. To carry out the analysis for the steady state motion, after the discretization of the Lagrangian function and the derivation of the linearized equations of motion,  some numerical results are obtained and compared, showing the impact of the elastic displacements on the spacecraft attitude motion.
 

Roma, A.M.; Lourenção, P.T.M.: On the dynamics of a satellite containing reaction wheels and deployable flexible solar arrays, Proceedings of the 1st Brazilian Symposium of Aerospace Technology, São José dos Campos, SP, Brazil, 08/30, 1990.